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Systems of linear ordinary differential equations are examined, subject to real-random parametric uncertainty. Specifically, the paper considers stability and norm-computation for this class of systems. The main finding is: do not apply Galerkin projection based polynomial chaos to such uncertain linear systems. Just use sampling-based methods instead, for instance, Gaussian quadrature. [ABSTRACT FROM AUTHOR]

In linear regulation theory, it is well-known that embedding in the control loop a suitable internal model of the exogenous disturbances and references permits to achieve perfect regulation of the desired variables robustly with respect to parametric uncertainties in the plant's equations. However, it was recently proved that this principle does not extend, in general, to nonlinear systems or non-parametric perturbations. Indeed, there exist systems for which no smooth finite-dimensional regulator can exist that regulates the desired variables to zero in spite of unstructured uncertainties affecting the plant's dynamics. This article complements such a negative result by proving that, in the canonical context of minimum-phase normal forms, a nonlinear regulator of the Luenberger type that guarantees robust asymptotic regulation with respect to unstructured uncertainties and possesses a star-shaped attractor necessarily behaves as a linear system on such an attractor. This result further strengthens the conjecture that robust regulation is essentially a linear property. [ABSTRACT FROM AUTHOR]

By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide conclusive affirmative answers to many analysis and design questions in systems and control. When these methods fail to produce a feasible solution, however, they often remain inconclusive due to (a) the method being conservative or (b) the fact that there may be multiple causes for infeasibility, such as ill-conditioning, solver tolerances or true infeasibility. To overcome this, we develop linear-matrix-inequality-based theorems of alternatives based upon which we can guarantee, by computing a so-called certificate of nonexistence, that no poly-quadratic Lyapunov function exists for a given linear parameter-varying system. We extend these ideas to also certify the nonexistence of controllers and observers for which the corresponding closed-loop/error dynamics admit a poly-quadratic Lyapunov function. Finally, we illustrate our results in some numerical case studies. [ABSTRACT FROM AUTHOR]

This paper proposes a robust formation control scheme for networked multi-tilt tricopter UAVs utilizing the Negative Imaginary (NI) and Positive Real (PR) theory. A Sliding Mode Control (SMC) scheme is designed for a multi-tilt tricopter to ensure stable hovering at a desired height. Then, a modified Subspace-based system identification algorithm is devised to identify a six-by-six NI model of the inner-loop-SMC-controlled tricopter in the continuous-time domain by exploiting the Laguerre filter. A two-loop formation control scheme has been developed for networked multi-tilt tricopters where the inner loop of each tricopter applies the SMC scheme, and the outer loop implements a distributed output feedback controller that satisfies the 'mixed' Strictly NI (SNI) + Strictly PR (SPR) system properties. Subsequently, we have established the robustness of the proposed scheme against NI/PR-type uncertainties and sudden loss of agents. The eigenvalue loci (also known as characteristic loci) technique is used instead of the Lyapunov-based approach to prove the asymptotic stability of the formation control scheme. An in-depth simulation case study was performed on a group of six inner-loop-SMC-controlled multi-tilt tricopters connected via a network to achieve a formation control mission, even in the presence of uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example. [ABSTRACT FROM AUTHOR]

The paper develops a methodology for the design of coherent equalizing filters for quantum communication channels. Given a linear quantum system model of a quantum communication channel, the aim is to obtain another quantum system which, when coupled with the original system, mitigates degrading effects of the environment. The main result of the paper is a systematic equalizer synthesis algorithm which relies on methods of state–space robust control design via semidefinite programming. [ABSTRACT FROM AUTHOR]

This paper is about robust Model Predictive Control (MPC) for linear systems with additive and multiplicative uncertainty. A novel class of configuration-constrained polytopic robust forward invariant tubes is introduced, which admit a joint parameterization of their facets and vertices. They are the foundation for the development of novel Configuration-Constrained Tube MPC (CCTMPC) controllers that freely optimize the shape of their polytopic tube, subject to conic vertex configuration constraints, as well as associated vertex control laws by solving convex optimization problems online. It is shown that CCTMPC is—under appropriate assumptions—systematically less conservative than Rigid- and Homothetic- Tube MPC. Additionally, it is proven that there exist control systems for which CCTMPC is less conservative than Elastic Tube MPC, Disturbance Affine Feedback MPC, and Fully Parameterized Tube MPC. [ABSTRACT FROM AUTHOR]

We propose a robust model predictive control (MPC) method for discrete-time linear systems with polytopic model uncertainty and additive disturbances. Optimizing over linear time-varying (LTV) state feedback controllers has been successfully used for robust MPC when only additive disturbances are present. However, it is challenging to design LTV state feedback controllers in the face of model uncertainty whose effects are difficult to bound. To address this issue, we propose a novel approach to over-approximate the effects of both model uncertainty and additive disturbances by a filtered additive disturbance signal. Using the System Level Synthesis framework, we jointly search for robust LTV state feedback controllers and the bounds on the effects of uncertainty online, which allows us to reduce the conservatism and minimize an upper bound on the worst-case cost in robust MPC. We provide a comprehensive numerical comparison of our method and representative robust MPC methods from the literature. Numerical examples demonstrate that our proposed method can significantly reduce the conservatism over a wide range of uncertainty parameters with comparable computational effort as the baseline methods. [ABSTRACT FROM AUTHOR]

A direct data-driven iterative algorithm is developed to accurately estimate the H ∞ norm of a linear time-invariant system from continuous operation, i.e., without resetting the system. The main technical step involves a reversed-circulant matrix that can be evaluated in a model-free setting by performing experiments on the real system. [ABSTRACT FROM AUTHOR]

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular model reduction, in which the subsystem models are reduced individually, is a practical and an efficient method to obtain accurate reduced-order models of such complex systems. However, when subsystems are reduced individually, without taking their interconnections into account, the effect on stability and accuracy of the resulting reduced-order interconnected system is difficult to predict. In this work, a mathematical relation between the accuracy of reduced-order linear-time invariant subsystem models and (stability and accuracy of) resulting reduced-order interconnected linear time-invariant model is introduced. This result can subsequently be used in two ways. Firstly, it can be used to translate accuracy characteristics of the reduced-order subsystem models directly to accuracy properties of the interconnected reduced-order model. Secondly, it can also be used to translate specifications on the interconnected system model accuracy to accuracy requirements on subsystem models that can be used for fit-for-purpose reduction of the subsystem models. These applications of the proposed analysis framework for modular model reduction are demonstrated on an illustrative structural dynamics example. [ABSTRACT FROM AUTHOR]

We present a robust nonlinear model predictive control (NMPC) algorithm for dynamic systems with mixed degrees of freedom, i.e., continuous and discrete manipulated variables. The discrete variables are often excluded from the NMPC layer and determined at a supervisory layer, which typically leads to suboptimal solutions. In contrast, the proposed controller optimizes both classes of degrees of freedom within the NMPC layer, thereby enhancing the closed-loop performance. Our approach relies on a computationally efficient relaxation and integrality restoration strategy. Initially, a nominal controller computes relaxed central reference trajectories for the states and the input variables. These trajectories are then tracked by an ancillary NMPC controller before the integrality of the discrete variables is restored. The role of the ancillary controller is to ensure robustness against the integer restoration error as well as other disturbances based on a nonlinear Tube MPC approach. Furthermore, we provide sufficient conditions to establish recursive feasibility and guarantee robust closed-loop stability. Finally, the effectiveness of the approach is demonstrated through two nonlinear simulation examples, affirming its viability and robustness. [ABSTRACT FROM AUTHOR]

This work proposes an approach to replace the use of a robust control invariant set by a pair of simpler sets that provide an inner and an outer approximation of the former. In the proposed approach, the outer set plays the role of the target region and the inner set is such that the trajectories that start inside it can be kept inside the outer set and be driven back to the inner set within a finite-time horizon. We show that the existence of these two sets implies the existence of a robust control invariant set between both regions. We also provide results that allow finding an inner set from a given target outer set and we show a way of using both sets in Model Predictive Control schemes such that the target region is never abandoned in spite of the fact that nor that region neither the inner set are invariant. We also illustrate the ideas with an example in which the inner and outer sets are very simple notwithstanding that any robust invariant set is not convex. [ABSTRACT FROM AUTHOR]

This work addresses formation containment control for a heterogeneous multi-agent system composed of first-order (FO) and second-order (SO) agents that can be either leader or follower agents. It is assumed that unknown but bounded disturbances perturb its dynamical model. An error-based version of a generalized proportional–integral observer (GPIO) is proposed to estimate these perturbations, and saturation functions, based on position measurement and estimated velocity errors, are designed to achieve the control objective. Specifically, it is shown that the leader agents converge to a desired geometric pattern following a desired trajectory simultaneously. Furthermore, the follower agents converge to the convex hull spanned by the leaders. The result applies to a group of robots in which a directed spanning tree gives the communication topology among the leaders with a root in the main leader. At the same time, each follower receives information from at least one leader agent, and the communication is directed. Real-time experiments and a comparison with a robust control technique exhibit the excellent performance of the proposed GPIO and control strategy in achieving formation containment control. [ABSTRACT FROM AUTHOR]

The robust control problem for systems with control coefficients without a constant sign and not separated from zero is addressed. It is shown that persistence of excitation conditions for the modulus of the control gain are sufficient to ensure stability of the system and matching conditions for the disturbance are sufficient to ensure finite-time stability, in the discontinuous case. Additionally, it is shown that finite-time convergent homogeneous controllers can guarantee uniform ultimate boundedness of the solutions even in the presence of mismatched disturbances and persistence of excitation conditions for the modulus of the control gain. [ABSTRACT FROM AUTHOR]

A computationally efficient reformulation of the rigid tube model predictive control is developed. A unique feature of the derived formulation is the utilization of the implicit set representations. This novel formulation does not require any set algebraic operations to be performed explicitly, and its implementation requires merely the use of the standard optimization solvers. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consensus problem of second-order multiagent systems under directed graphs. Simple yet robust consensus algorithms that advance existing achievements in accounting for velocity and input constraints, agent uncertainties, and lack of neighboring velocity measurements are proposed. Furthermore, we show that the proposed method can be applied to the consensus control of uncertain robotic manipulators with velocity and control torque constraints. We rigorously prove that the velocity and control inputs stay within prespecified ranges by tuning design parameters a priori and that asymptotic consensus can be achieved through Lyapunov functions and fixed-time stability. Simulations are performed for symmetric and asymmetric constraints to show the efficiency of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the trajectory tracking control problem of a class of uncertain Euler–Lagrange systems subject to disturbances. In sharp contrast to existing approaches where the position, the velocity, and the acceleration of the reference trajectory are assumed to be measurable, we propose a class of dynamic output feedback control laws which depends on the tracking error of the position and that of the velocity. Specifically, by characterizing the reference trajectory and the disturbances with an exosystem, we design an internal model to learn the desired feedforward input such that the reference trajectory can be tracked in spite of unknown system parameters and disturbances. The effectiveness of the proposed approach is illustrated by its application to trajectory tracking control of a three-link cylindrical robot arm. [ABSTRACT FROM AUTHOR]

This paper deals with the robust recursive regulation problem of uncertain discrete-time linear systems subject to unknown state delays. The variation rate between two consecutive delays is considered bounded. The parameter matrices are affected by norm-bounded uncertainties. Applying the lifting method and modeling the delay as a Markov chain, systems with state delays are converted to augmented delay-free Markovian jump linear systems. Then, a robust recursive linear quadratic regulator is obtained, solving an optimization problem through robust regularized least-squares approaches. The solution is given in terms of algebraic Riccati equations. We assess the proposed regulator through a numerical example and compare its performance with other robust control approaches. [ABSTRACT FROM AUTHOR]

This study addresses the problem of robust tracking control of vertical take-off and landing (VTOL) unmanned aerial vehicles through a vision-based control technique. The main objective is to design a new theoretical result for vision-based tracking of a moving target in the presence of external disturbances. In particular, the proposed control framework is able to simultaneously guarantee a saturated thrust input, and measurable and bounded desired angular velocity and acceleration while dealing with time-varying disturbances in the dynamics of the system. Considering different sets of visual features, two control schemes are proposed, where the features are defined based on perspective image moments. Simulation studies are conducted in perturbed conditions to verify the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Robustness to uncertainties is one of the main challenges in model-based fault diagnosis. Robust fault diagnosis is a mature research area for Ordinary Differential Equation (ODE) systems. However, robust diagnostics for systems modeledby Partial Differential Equations (PDEs) is significantly under-explored in existing literature. Spatio-temporal evolution of faults make PDE fault diagnosis more challenging, as compared to its ODE counterpart where the fault evolves only temporally. Furthermore, robustness to uncertainties, that is, distinguishing the effect of uncertainties from faults is another key design challenge in fault diagnosis. This paper presents a robust fault diagnosis scheme for a class of uncertain linear parabolic PDEs. The proposed scheme consists of two subsystems: (i) Residual Generator and, (ii) Adaptive Threshold Generator. The Residual Generator is a PDE observer whose output error is treated as a residual signal. Ideally, the residual signal should be zero if there is no fault and non-zero otherwise. However, the residual signal is non-zero even under non-faulty conditions, due to the presence of uncertainties. To achieve robustness against such uncertainties, we design a novel Adaptive Threshold Generator that generates an adaptive threshold. Finally, we illustrate the proposed scheme via simulation case studies on battery thermal fault detection. [ABSTRACT FROM AUTHOR]

This paper develops a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. The resulting piecewise constant control inputs achieve communication reduction and guarantee constraint satisfactions. In the particular case when there is no uncertainty, we propose a control design with minimum number of samplings over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as computationally tractable mixed integer linear programs. The method is compared with the robust self-triggered model predictive control in a numerical example and applied to a robot motion planning problem with temporal constraints. [ABSTRACT FROM AUTHOR]

We propose a set-valued controller with a signum multifunction nested inside another one. We prove that the controller is well posed and achieves robust ultimate boundedness in the presence of mismatched, non-vanishing disturbances. Even more, the selected output can be made arbitrarily small. Also, by applying an implicit/explicit Euler scheme similar to the one introduced by Acary and Brogliato (2010) for matched disturbances, we derive a selection strategy for the discrete-time implementation of the set-valued control law. Simulations demonstrate that the discrete scheme diminishes chattering substantially, compared with a fully explicit method. [ABSTRACT FROM AUTHOR]

In this paper, we study the robust trajectory tracking problem for a class of nonlinear systems with incremental passivity. The velocity of the desired trajectory and parts of the model information are unknown apart from boundedness assumptions. A velocity observer based method and a sliding mode controller are proposed while the asymptotic tracking result is guaranteed by a zero-state detectability condition for both cases. Unlike previous results, the studied systems are not necessarily feedback linearizable nor in a strict feedback form. The ball and beam system is utilized to illustrate the implementation of the proposed tracking control laws. [ABSTRACT FROM AUTHOR]

This work is an attempt to establish a probabilistic framework for the assessment and design of observer-based fault detection systems. The fundament of our study is randomized algorithms methods which are successfully applied to deal with uncertainty issues in robust control. For our purpose, probabilistic parameter models for faults and model uncertainties are first introduced. The main focus of our work is on the development of randomized algorithms for the assessment of false alarm rate, fault detection rate and mean time to detection as well as for the design of observer-based fault detection systems. To illustrate the potential applications of the proposed algorithms and methods, benchmark study on a real three-tank system is included. [ABSTRACT FROM AUTHOR]

In this paper, entirely new discrete-time variants of the super-twisting algorithm are presented. The development of these discrete-time equivalents is based on certain criteria, e.g., the approximation of the continuous-time super-twisting algorithm as the discretization time tends to zero. In contrast to the classical explicit Euler discretized super-twisting dynamics, the proposed schemes are exact in the sense that in the unperturbed case, the controllers ensure local convergence to the origin. Oscillations of the system states caused by the discrete-time implementation of the super-twisting algorithm are avoided. The superiority of the developed control laws is demonstrated in simulation examples as well as in a real-world application. These examples reveal that the standard accuracy of the homogeneous second-order sliding mode is preserved and, in contrast to the explicit Euler discretized algorithm, in the presence of exact discrete measurements, the precision of the controlled variable is insensitive to oversized control gains. [ABSTRACT FROM AUTHOR]

This technical communique studies the robust output regulation problem of uncertain discrete-time linear systems by quantized output feedback control. We show that, under the same assumptions as those that guarantee the solvability of the robust output regulation problem by a dynamic output feedback control law, our problem is also solvable by a dynamic quantized output feedback control law as long as the quantization density is greater than certain explicitly specified lower bound. [ABSTRACT FROM AUTHOR]

Multi-agent systems under temporal logic tasks have great potential due to their ability to deal with complex tasks. The control of these systems, however, poses many challenges and the majority of existing approaches result in large computational burdens. We instead propose computationally-efficient and robust feedback control strategies for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design. A bottom-up scenario is considered in which each agent is subject to a local task from a limited signal temporal logic fragment. Notably, the satisfaction of a local task may also depend on the behavior of other agents. We provide local continuous-time feedback control laws that, under some sufficient conditions, guarantee satisfaction of the local tasks. Otherwise, a local detection & repair scheme is proposed in combination with the previously derived feedback control laws to deal with infeasibilities, such as when local tasks are conflicting. The efficacy of the proposed method is demonstrated in simulations. [ABSTRACT FROM AUTHOR]

This paper focuses on comparing fault detection (FD) conservatism of the set-theoretic unknown input observer (SUIO) based method and the interval observer (IO) based method. The former is implemented by combining both the set theory and the unknown input observer (UIO), where the set theory and the UIO are used to decouple disturbances and noises in passive and active ways, respectively. The latter is based on the set theory and the Luenberger-structure observer, which completely relies on the set-based passive decoupling of disturbances and noises to obtain FD robustness. The objective of this paper is to compare their FD conservatism using systematic mathematical analysis based on zonotopes and a mathematical criterion comparing their FD conservatism is obtained. Moreover, by establishing a general residual framework for conservatism analysis, the proposed method comparing the FD conservatism is also extended to compare the FD conservatism of a wide variety of set-based robust FD methods. At the end of this paper, a two-tank system example is used to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This brief is concerned with the formation control problem of a multi-agent system composed of multiple quadrotors tasked to achieve aggressive trajectory tracking with prescribed formation patterns. An underactuated model with six degrees of freedom is considered for each quadrotor, the dynamics of which account for nonlinearities, parameter uncertainties, and external disturbances. A robust control approach is proposed that stems from linear quadratic regulation and robust compensation theory fundamentals. Theoretical analysis and simulation results validate the effectiveness of the presented theoretical framework. [ABSTRACT FROM AUTHOR]

There is an increasing trend to apply integrated mechatronic design approaches in precision engineering to synthesize key mechanical and controller parameters simultaneously. However, such technique is yet to be mature, due to the constraints imported by mechanical design and feedback control, as well as the existence of model uncertainties. In this work, we treat the integrated mechatronic design problem as a controller optimization problem with structural constraints. We start from the case when the composite feedback gain matrix (CFGM) has some elements either being zero or with equal or opposite relationships. First, algorithms are proposed to factorize the CFGM. Secondly, the feedback constraints are transformed from the state space to an extended parameter space. In this way, the design problem is reformulated as minimizing the ℋ 2 -norm upper bound of the closed-loop system transmittance from the exogenous disturbance to the regulated variables over the intersection of convex and non-convex domains. Eventually, cutting-plane-based numerical procedures are developed to obtain a global optimal solution, and the closed-loop robust stability is ensured with guaranteed performance. An illustrative example on a flexure-linked biaxial gantry stage is presented to reveal the practical appeal of the proposed approach. This approach is extensively applicable to a class of optimal control problems, such as controller synthesis problem with prescribed sparsity pattern, decentralized control problem with/without structural constraints, etc. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the study of strictly negative imaginary (SNI) systems and the problem of synthesizing a controller rendering a linear fractional system SNI. First, a set of necessary and sufficient conditions are developed for an SNI lemma without imposing minimality assumptions. The proposed lemma supports both the analysis and synthesis of SNI systems. Then, a set of sufficient conditions, based on the solution of algebraic Riccati equations, is provided for the solution of the SNI synthesis problem. Finally, an illustrative example demonstrates the usefulness of the results given herein. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the problem of robust tracking control for quasilinear reaction–diffusion partial differential equations subject to external unknown perturbations. The considered class of equations is quite general, and includes classical equations such as the heat equation or the Fisher–KPP equation as special cases. Global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite-dimensional sliding-mode controller. Extensive simulations support and validate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE (3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract Robust constrained control of linear systems with parametric uncertainty and additive disturbance is addressed. The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism. Requirements for closed-loop stability and provable constraint satisfaction are considered separately, resulting in the use of online set-membership system identification combined with homothetic prediction tubes for robust constraint satisfaction, and an H ∞ optimal point estimate of the unknown parameters to achieve a finite closed-loop gain from the disturbance to the state. Extensions to time-varying parameters and persistently exciting inputs to guarantee parameter convergence are presented. A numerical example illustrates the proven properties and efficacy of the approach. [ABSTRACT FROM AUTHOR]

Abstract This paper describes a novel scheme for fault tolerant control using a robust optimal control design method. This scheme can also be employed as actuator redundancy management for over-actuated linear systems. In contrast to many existing methods in the literature, this scheme can be applied to systems whose control input matrix cannot be factorised into two matrices whose ranks are equal and less than the minimum of the number of columns and rows of the input matrix. The so-called virtual control, in this scheme, is calculated using a robust ℋ 2 -based feedback design approach constructed to be robust against uncertainties emanating from visibility of the control allocator to the controller and imperfection in the estimated effectiveness gain. Then, using a new control allocation scheme along with a novel Tikhonov-based re-distributor mechanism, the obtained virtual control signal is re-distributed among remaining (redundant or non-faulty) set of actuators. As the proposed scheme is modular-based, it can be employed as a real-time fault tolerant control scheme with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed scheme is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the problem of robust H ∞ filtering for discrete-time systems with Lipschitz nonlinearities and uncertain parameters. Both the cases of systems subject to either polytopic or norm-bounded parameter uncertainties are treated and it is considered that all the matrices of the system state-space model can be affected by uncertain parameters. Novel methods in terms of linear matrix inequalities are proposed for designing nonlinear filters with a general structure that ensure global exponential stability of the estimation error dynamics and a prescribed (or optimized) H ∞ performance for all admissible uncertain parameters. In the case of polytopic uncertain systems, the filter design is based on an affine uncertainty-dependent Lyapunov function. Numerical examples are presented to illustrate the effectiveness of the proposed robust H ∞ filtering methods. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the robust cooperative output regulation problem of uncertain linear multi-agent systems with additive disturbances via the celebrated internal model principle. Two novel distributed controllers are designed based on the adaptive control strategy and the event-triggered transmission scheme, where the adaptive control strategy is utilized to avoid the requirement for a priori knowledge of the minimal nonzero eigenvalue of the Laplacian matrix associated with the communication topology, and the event-triggered transmission scheme is utilized to reduce the frequency of data transmission. It is shown that the proposed control schemes achieve robust cooperative output regulation asymptotically and Zeno behavior is excluded. Finally, a simulation example is presented to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Abstract In this paper, robust fault estimation and fault tolerant control for stochastic Takagi–Sugeno fuzzy systems, subjected to Brownian parameter perturbations, unknown process uncertainties and unexpected faults, are investigated. Augmented system approach, unknown input observer techniques and sliding mode control strategies are integrated to decouple the influences from the unknown input uncertainties, and drive the trajectories of the estimation error dynamics to enter and subsequently remain within a desired surface of the error space. As a result, a robustly simultaneous estimate of the means of the faults concerned and the full system states can be achieved. In the meanwhile, the actuator/sensor signal compensation techniques are used to formulate the tolerant control strategy to eliminate or offset the influences from the faults to the systems dynamics and ensure the robust stabilization of the closed-loop control system. In terms of linear matrix inequalities, sufficient conditions are proposed to ensure the robust stability of the overall closed-loop system composed of system state and estimation error dynamics, as well as the reachability of the sliding mode surface. Furthermore, the systematic design procedures for the robust fault estimation and fault tolerant control scheme are addressed. Finally, simulation studies on a single-link manipulator and a three-tank system are illustrated to demonstrate the effectiveness of the suggested methodologies. [ABSTRACT FROM AUTHOR]

Abstract Control systems that satisfy temporal logic specifications have become increasingly popular due to their applicability to robotic systems. Existing control methods, however, are computationally demanding, especially when the problem size becomes too large. In this paper, a robust and computationally efficient model predictive control framework for signal temporal logic specifications is proposed. We introduce discrete average space robustness, a novel quantitative semantic for signal temporal logic, that is directly incorporated into the cost function of the model predictive controller. The optimization problem entailed in this framework can be written as a convex quadratic program when no disjunctions are considered and results in a robust satisfaction of the specification. Furthermore, we define the predicate robustness degree as a new robustness notion. Simulations of a multi-agent system subject to complex specifications demonstrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the robust cooperative output regulation problem via measurement feedback for a class of linear multi-agent systems, which is not detectable by regulated output. To solve it, necessarily additional measurement is assumed to be available, and the normal form defined on the additional measurement is utilized. Under mild assumptions on the communication network and the zero dynamics, a novel distributed measurement feedback controller can be established, consisting of the distributed dynamical compensator, internal model and possibly asymptotic observer , such that all regulated errors can globally exponentially converge to zero. Only regulated output of each agent needs to be transmitted to its neighbors, while neither the plant state nor the controller state is required to be exchanged with its neighbors. [ABSTRACT FROM AUTHOR]

Abstract Cyber–physicalempirical methods consist in partitioning a dynamical system under study into a set of physical and numerical substructures that interact in real-time through a control system. In this paper, we define and investigate the fidelity of such methods, that is their capacity to generate systems whose outputs remain close to those of the original system under study. In practice, fidelity is jeopardized by uncertain and heterogeneous artefacts originating from the control system, such as actuator dynamics, time delays and measurement noise. We present a computationally efficient method, based on surrogate modelling and active learning techniques, to (1) verify that a cyber–physical empirical setup achieves probabilistic robust fidelity, and (2) to derive fidelity bounds, which translate to absolute requirements to the control system. For verification purposes, the method is first applied to the study of a simple mechanical system. Its efficiency is then demonstrated on a more complex problem, namely the active truncation of slender marine structures, in which the substructures' dynamics cannot be described by an analytic solution. [ABSTRACT FROM AUTHOR]

Abstract We discuss robust representations of stable, passive systems in particular coordinate systems, focussing especially on port-Hamiltonian representations. Such representations are typically not unique and the degrees of freedom associated with nonuniqueness are related to the solution set of the Kalman–Yakubovich–Popov linear matrix inequality (LMI). In this paper we analyze robustness measures for different possible port-Hamiltonian representations and relate it to quality functions defined in terms of eigenvalues of the matrix solution of the LMI. In particular, we look at the analytic center of this LMI. Within this framework, we derive inequalities for the passivity radius of the given model representation. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the event-triggered distributed predictive control (DPC) problem for multi-agent systems subject to bounded disturbances. A novel event-triggering mechanism which involves the neighbours' information is derived for each agent to achieve a trade-off between resource usage and control performance. In such a framework, the DPC optimization problem is solved and information is exchanged only at triggering instants, thus achieving asynchronous coordination. To lower computation and communication consumption more significantly, a dynamic variable considering effects of neighbours is introduced to design a dynamic event-triggering condition and we show that larger inter-execution time can be obtained using the dynamic triggering mechanism. The theoretical conditions on ensuring feasibility and closed-loop stability are developed for these two triggering mechanisms, respectively. Finally, numerical simulations are given to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Abstract We investigate the performance and robustness of distributed averaging integral controllers used in the optimal frequency regulation of power networks. We construct a strict Lyapunov function that allows us to quantify the exponential convergence rate of the closed-loop system. As an application, we study the stability of the system in the presence of disruptions to the controllers' communication network, and investigate how the convergence rate is affected by these disruptions. [ABSTRACT FROM AUTHOR]

Abstract Motion planning of multi-robot systems has been extensively investigated. Many proposed approaches assume that all robots are reliable. However, robots with priori known levels of reliability may be used in applications to account for: (1) the cost in terms of unit price per robot type, and (2) the cost in terms of robot wear in long term deployment. In the former case, higher reliability comes at a higher price, while in the latter replacement may cost more than periodic repairs, e.g., buses, trams, and subways. In this study, we investigate robust control of multi-robot systems, such that the number of robots affected by the failed ones is minimized. It should mandate that the failure of a robot can only affect the motion of robots that collide directly with the failed one. We assume that the robots in a system are divided into reliable and unreliable ones, and each robot has a predetermined and closed path to execute persistent tasks. By modeling each robot's motion as a labeled transition system, we propose two distributed robust control algorithms: one for reliable robots and the other for unreliable ones. The algorithms guarantee that wherever an unreliable robot fails, only the robots whose state spaces contain the failed state are blocked. Theoretical analysis shows that the proposed algorithms are practically operative. Simulations with seven robots are carried out and the results show the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

Abstract In this paper, an adaptive output feedback compensation control scheme is proposed for a class of nonlinear systems with unknown sensor failures. For estimating the unmeasured states, a novel switching-type adaptive observer is constructed, in which the observer gains are tuned in a switching manner. To compensate for the failure effects on transient performance, a new error signal which contains an adaptive compensation coefficient is introduced into backstepping procedure. It is shown that the proposed controller can guarantee the closed-loop system is globally uniformly ultimately bounded, and system output converges to an adjustable neighborhood of the origin. Simulation results are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A robust hierarchical model predictive control framework is presented for controlling a linear system of dynamically coupled subsystems. A graph-based modeling framework captures the conservation laws of power flow systems, for which control optimizes the storage and routing of energy to maximize transient and steady-state power throughput. A constructive approach is presented for developing an N -level hierarchical controller, which guarantees satisfaction of state and input constraints in the presence of signal and model uncertainty. [ABSTRACT FROM AUTHOR]

Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V ̇ < 0 , if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles non-convex constraints and disturbances and to illuminate some tradeoffs. [ABSTRACT FROM AUTHOR]

A linear switched system with bounded unknown inputs is considered in this paper. The study of the controlled distinguishability (or discernibility) property of the operating modes of the system is addressed. This property ensures the existence of a control input that generates different output signals of the modes regardless of the initial state vector and the unknown inputs. Such control inputs are called discerning controls. The robustness problem of the discerning controls with respect to the unknown inputs is analyzed, namely: under which conditions does a discerning control of the unknown-input-free modes remains a discerning control for the perturbed modes? To solve this problem, the existence of a quantifier measuring the size of the unknown inputs that discerning controls of the unknown-input-free modes have to be robust to in order to remain discerning controls for the perturbed modes is shown. In addition to this robustness result, an algorithm is proposed to design discerning controls for perturbed modes. Finally, from this input design procedure it is proven that when bounded unknown inputs are considered, there is an equivalence between controlled distinguishability of the unknown-input-free modes and that of the perturbed modes. [ABSTRACT FROM AUTHOR]